68 citations · 577 across the 31 of their papers we have counts for
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The Derivation of the Boltzmann Equation from Quantum Many-body Dynamics
Xuwen Chen, Justin Holmer
We consider the quantum many-body dynamics at the weak-coupling scaling. We derive rigorously the quantum Boltzmann equation, which contains the classical hard sphere model and, ef…
Sharp Global Well-posedness and Scattering of the Boltzmann Equation
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We consider the 3D Boltzmann equation for the Maxwellian particle and soft potential with an angular cutoff. We prove sharp global well-posedness with initial data small in the sca…
Well/Ill-posedness of the Boltzmann Equation with Soft Potential
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We consider the Boltzmann equation with the soft potential and angular cutoff. Inspired by the methods from dispersive PDEs, we establish its sharp local well-posedness and ill-pos…
On the mean-field and semiclassical limit from quantum -body dynamics
Xuwen Chen, Shunlin Shen, Zhifei Zhang
We study the mean-field and semiclassical limit of the quantum many-body dynamics with a repulsive -type potential and a Coulomb potential, which leads to a macr…